Is there a black hole information paradox in string theory? In string theory there is, for several black hole-like objects, a precise way to account for the microstates which make up the macroscopic Bekenstein-Hawking entropy. For instance for the black brane made of a bound state of $Q_1$ D1- and $Q_5$ D5-branes wrapped on $T^4 \times S^1$ the (1,5) and (5,1) open strings provide the leading contribution to the entropy at large charges, which is exactly $A/4$. 
How, if at all, is the information paradox solved in this example or examples like this? What is the mechanism by which a pure in-state evolves into a thermal density matrix out-state-- and what happens in between? 
 A: No. There is no information paradox in string theory.
The example you cite (the D1-D5 system) is a stable BPS configuration, so no evaporation is taking place and all the black hole microstates (correctly computed by string theory) are evolving unitarily because string theory does not modify the rules of quantum mechanics ( see the beautiful Motl's post Why string theory is quantum mechanics on steroids).
The fact that we perceive a black hole with a unique macroscopic state in the supergravity approximation as follows from higher-dimensional no-hair theorems (sometimes violated in string theory) is just an artifact produced by the fact that higher string modes are integrated out (by definition of zero-slope limit) but after all stringy modes are taken into account, no loss of coherence is possible.
But even if you allow evaporating black holes in string theory, information is preseverved because all the objects in string theory evolve unitarily. Even in time dependent situations, string theory predict the correct entropy computation (beautiful example). Even if you take into account non-perturbative corrections , or you analize Calabi-Yau black holes outside the OSV regime (as was done in here and here) you will never find loss of coherence.
Arguably the most clear examples of the absence of information-like paradoxes in string theory are black holes realized within M(atrix) theory (example) because the BFSS theory is manifestly an "ordinarily" quantum mechanical model.
